Challenge Yourself #CHAPTER3

A * H is a set of _____ coset.
Right
Left
Sub
Semi
a * H = H * a relation holds if __________.
H is semigroup of an abelian group.
H is monoid of a group.
H is a cyclic group.
H is subgroup of an abelian group.
A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called ____________.
Isomorphic
Homomorphic
Cyclic group
Heteromorphic
An isomorphism of a group onto itself is called ____________.
Homomorphism
Heteromorphism
Epimorphism
Automorphism
The homomorphism of a group onto itself is defined as the ___________.
Endomorphism
Homomorphism
Automorphism
Heteromorphism
The elements of a vector space form a/an ____________ under vector addition.
abelian group
Commutative group
Associative group
semigroup
A set of representatives of all the cosets is called _________.
Transitive
Reversal
Equivalent
Transversal
Which of the following statement is true?
The set of all matrices forms a group under multiplication.
The set of all rational negative numbers forms a group under multiplication.
The set of all non-singular matrices forms a group under multiplication.
The set of matrices forms a subgroup under multiplication.
How many different non-isomorphic Abelian groups of order 8 are there?
5
4
2
3
Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________.
does not form a group
does not have the right identity element
Forms a non-commutative group
Forms a group if the empty string is removed from
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